Question

Please post all the work so I can understand the process! Thanks :)

In a large corporation, 70% of the employees are male. A random sample of five employees is selected. Assume a binomial distribution.

a.	What is the probability that the sample contains exactly three male employees?
b.	What is the probability that the sample contains no male employees?
c.	What is the probability that the sample contains more than three female employees?
d.	What is the expected number of female employees in the sample?

Answer 1

This is a binomial distribution

p = 0.7

n = 5

P(X = x) = 5Cx * 0.7^x * (1 - 0.7)^5-x

a) P(X = 3) = 5C3 * 0.7³ * 0.3² = 0.3087

b) P(X = 0) = 5C0 * 0.7⁰ * 0.3⁵ = 0.0024

c) now, p = P(female) = 1 - P(male) = 1 - 0.7 = 0.3

P(X > 3) = P(X = 4) + P(X = 5)

              = 5C4 * 0.3⁴ * 0.7¹ + 5C5 * 0.3⁵ * 0.7⁰

              = 0.0308

d) Expected number = n * p = 5 * 0.3 = 1.5